What 3-digit number is a perfect square and a perfect cube?

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What 3-digit number is a perfect square and a perfect cube?

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Answer 1 · 2015-06-28T07:03:05

$729 = 9^{3} = 27^{2}$ $729=9^3=27^2$

Explanation:

The answer must be $a^{6}$ $a^6$ for some integer $a$ $a$ due to the properties of exponentiation. Only $3^{6} = 729$ $3^6 = 729$ lies in the required range.

$3^{6} = {(3^{2})}^{3} = 9^{3}$ $3^6 = (3^2)^3 = 9^3$

$3^{6} = {(3^{3})}^{2} = 27^{2}$ $3^6 = (3^3)^2 = 27^2$

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What 3-digit number is a perfect square and a perfect cube?

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